Robotics and Mechanisms Laboratory

Dexterity Measures

The Jacobian matrix of a parallel manipulator is used to relate the end effector velocity vector to a vector of actuator velocities. The singular values and condition number of this matrix are ideal measurements of dexterity. However, for complex degree of freedom manipulators, dimensional inconsistencies within the Jacobian matrix prohibit the use of such dexterity indices.

A method of developing a Jacobian matrix that relates independent Cartesian velocities of points on the end effector to actuator velocities is introduced. In the typical case where the number of independent Cartesian velocities is equal to the number of actuators, the resulting Jacobian matrix is square and dimensionally consistent. The formulation of such a Jacobian matrix is demonstrated for a variety of complex degree of freedom manipulators. The Jacobian matrix is then used to determine dexterity, and finally, obtain information regarding the dexterous workspace characteristics of that particular manipulator. Formulating a constrained and dimensionally-homogeneous Jacobian matrix and using it to obtain dexterous workspace information requires the formulation of the inverse displacement solution using a different selection of independent end effector velocities and identifying singular configurations. A screw based Jacobian matrix is also formulated in order to verify results obtained by the proposed method. The various workspaces corresponding to each manipulator may then be compared in order to determine which is best suited for particular applications.